You can use a summation of areas of rectangles under the graph.
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Width of each rectangle will be: \[w={{b-a}\over n}\]Where b=right limit=2
a=left limit=-2
n=number of rectangles.
Then: \[\sum_{n=1}^{n} w f(a+wn)\]
But because the graph goes into the negative you'll need to find the area of -2<=x<=0 and add on the area of 0<=x<=2 to get the total area.